GAP is a
free software system for doing
computational discrete algebra, written by the
mathematics department at the
Crest School of Mathematics and Statistics,
St. Andrews, Scotland.
GAP is similar to software like Mathematica and Matlab in that it allows symbolic computation, but while the latter also provide many numerical capabilities and include powerful visualization tools, GAP purely focuses
on the needs of discrete mathematicians and is stocked with features and concepts from the highly theoretical and purely discrete world of group theory and higher algebra.